Estimating the Mean of a Population

[Estimating the Mean of a Population]

NARRATOR: Many of the research situationsdiscussed in this video series involve a population mean mu.The value of mu is stated in the null hypothesis.For example, mu could be equal to some value,or it could be that the mu of one populationis equal to the mu of another population.In these research situations, you'll either reject or not

NARRATOR [continued]: reject the null hypothesis.It isn't always possible to state a value of mu,because we may not know what mu is.In situations such as this, we becomemore interested in estimating the value of mu.Imagine a political candidate is unsure how voters perceive her,and she wants to estimate the percentage of voters

NARRATOR [continued]: who view her favorably.Taking into account the possibility of error,she wants to create a range or interval of valuesthat contain the population mean with a desireddegree of confidence.This interval of values is what'sknown as a confidence interval.[Confidence Interval]Here's the formula for the confidenceinterval for the mean.This is an example of interval estimation.

NARRATOR [continued]: Interval estimation involves estimatingan unknown population parameter by specifying a rangeor interval of values within whichyou have a certain degree of confidence the populationparameter will fall.Interval estimation can be used in a varietyof research situations.In this video, we'll calculate the confidence intervalof the mean.

NARRATOR [continued]: This is an interval of values for a variable thathas a stated probability of containingan unknown population mean.The formula starts with a sample mean x bar.Creating the confidence interval for the mean means movingto the left and right of the samplemean so that you create an interval or a range of valuesthat has a stated confidence which contains

NARRATOR [continued]: the unknown population mean.You'll see we're not making a decision regardingthe population mean as a certain value.Instead, we're estimating what we thinkthe population mean might be.But just what is a confidence interval?Is it the probability of an interval, or the probabilityof a population mean?A confidence interval for the mean

NARRATOR [continued]: is an interval that has a stated probability of containingthe population mean.In other words, we could state that there is a 95% probabilitythat the interval from this to thiscontains the unknown population mean.When we do interval estimation, weidentify two scores, an upper and lower boundary.

NARRATOR [continued]: The interval between those two boundarieshas a 95% probability of containing the population mean.This implies that our interval will eithercontain the population mean or it will not,and we have identified the only twoscores for that sample that will contain the population mean95% of the time.